Dc is an arbitrary precision desk calculator. Ordinarily it operates
on decimal integers, but one may specify an input base, output
base, and a number of fractional digits to be maintained. The
overall structure of dc is a stacking (reverse Polish) calculator.
If an argument is given, input is taken from that file until its
end, then from the standard input. The following constructions
are recognized:
number

The value of the number is pushed on the stack. A number is an
unbroken string of the digits 0–9A–F or 0–9a–f. A hexadecimal number
beginning with a lower case letter must be preceded by a zero
to distinguish it from the command associated with the letter.
It may be preceded by an underscore _ to
input a negative number. Numbers may contain decimal points.

+ – / * % ^

Add +, subtract –, multiply *, divide /, remainder %, or exponentiate
^ the top two values on the stack. The two entries are popped
off the stack; the result is pushed on the stack in their place.
Any fractional part of an exponent is ignored.

sxSx Pop the top of the stack and store into a register named x,
where x may be any character. Under operation S register x is
treated as a stack and the value is pushed on it.lxLx Push the value in register x onto the stack. The register x
is not altered. All registers start with zero value. Under operation
L register x is treated as a stack and its top value is popped
onto the main stack.d Duplicate the top value on the stack.p Print the top value on the stack. The top value remains unchanged.
P interprets the top of the stack as a text string, removes it,
and prints it.f Print the values on the stack.q
Q Exit the program. If executing a string, the recursion level
is popped by two. Under operation Q the top value on the stack
is popped and the string execution level is popped by that value.x Treat the top element of the stack as a character string and
execute it as a string of dc commands.X Replace the number on the top of the stack with its scale factor.[ ... ]

Put the bracketed text string on the top of the stack.
<

x
>x=x Pop and compare the top two elements of the stack. Register
x is executed if they obey the stated relation.v Replace the top element on the stack by its square root. Any
existing fractional part of the argument is taken into account,
but otherwise the scale factor is ignored.! Interpret the rest of the line as a shell command.c Clear the stack.i The top value on the stack is popped and used as the number base
for further input.I Push the input base on the top of the stack.o The top value on the stack is popped and used as the number base
for further output. In bases larger than 10, each `digit' prints
as a group of decimal digits.O Push the output base on the top of the stack.k Pop the top of the stack, and use that value as a non–negative
scale factor: the appropriate number of places are printed on
output, and maintained during multiplication, division, and exponentiation.
The interaction of scale factor, input base, and output base will
be reasonable if all are changed together.
z Push the stack level onto the stack.Z Replace the number on the top of the stack with its length.? A line of input is taken from the input source (usually the terminal)
and executed.; : Used by bc for array operations.

The scale factor set by k determines how many digits are kept
to the right of the decimal point. If s is the current scale factor,
sa is the scale of the first operand, sb is the scale of the second,
and b is the (integer) second operand, results are truncated to
the following scales.